Analogy: vectors as colours
Colours can be encoded as a list of values [R, G, B], and we can conceptualize this as a more abstract type of vector. "Red", "green", and "blue" behave as our basis vectors from which we can construct all other colours by combining them in varying ratios. We can also have different basis sets such as the CMYK system. {C, M, Y} forms the basis set. I'm sure there's already an analysis on this in computer graphics!